Real-World Systems of Equations Quick Check

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Question
Solve this real-world problem using a system of equations. The O’Donnells are having a birthday party for their son, and they plan to have a clown bring balloons to the party. Balloon Express charges $2 per balloon and $10 for delivery. Balloon Mania charges $1.50 per balloon and $20 for delivery. If the O’Donnells plan to order 30 balloons, which company should they choose, and how much will they save?(1 point)
Responses

Balloon Mania; $25 
Balloon Mania; $25 

Balloon Express; $25
Balloon Express; $25

Balloon Mania; $5
Balloon Mania; $5

Balloon Express; $5

1 answer

To determine which balloon company the O’Donnells should choose, we can set up a system of equations to calculate the total cost for each company given that they plan to order 30 balloons.

  1. Balloon Express charges:

    • \(2\) dollars per balloon
    • \(10\) dollars for delivery

    The total cost for Balloon Express (\(C_E\)) can be calculated as: \[ C_E = (2 \times 30) + 10 = 60 + 10 = 70 \text{ dollars} \]

  2. Balloon Mania charges:

    • \(1.50\) dollars per balloon
    • \(20\) dollars for delivery

    The total cost for Balloon Mania (\(C_M\)) can be calculated as: \[ C_M = (1.50 \times 30) + 20 = 45 + 20 = 65 \text{ dollars} \]

Next, we compare the total costs:

  • Total cost for Balloon Express: \(C_E = 70\) dollars
  • Total cost for Balloon Mania: \(C_M = 65\) dollars

The difference in cost, or how much the O’Donnells would save by choosing Balloon Mania over Balloon Express, is: \[ \text{Savings} = C_E - C_M = 70 - 65 = 5 \text{ dollars} \]

Therefore, the O’Donnells should choose Balloon Mania and will save $5.

So the correct answer is: Balloon Mania; $5.